What do Geometric Hallucination Detection Metrics Actually Measure?

2026-02-09

AI Summary

Existing geometric hallucination detection metrics struggle to distinguish specific hallucination types in the absence of ground truth and are highly sensitive to domain shifts. This work addresses these limitations by constructing a synthetic dataset to systematically evaluate the capacity of various geometric statistics to capture key hallucination attributes—such as output correctness, relevance, and coherence—and reveals that different metrics align with distinct hallucination types. Furthermore, the study proposes a simple yet effective normalization strategy that substantially mitigates the impact of domain shift. Experimental results demonstrate that, under multi-domain settings, the proposed approach improves AUROC by 34 percentage points, significantly enhancing the cross-domain robustness of geometric hallucination detection metrics.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Computer Vision: Adversarial Attacks & Robustness
• Natural Language Processing: Safety and Robustness

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Hallucination remains a barrier to deploying generative models in high-consequence applications. This is especially true in cases where external ground truth is not readily available to validate model outputs. This situation has motivated the study of geometric signals in the internal state of an LLM that are predictive of hallucination and require limited external knowledge. Given that there are a range of factors that can lead model output to be called a hallucination (e.g., irrelevance vs incoherence), in this paper we ask what specific properties of a hallucination these geometric statistics actually capture. To assess this, we generate a synthetic dataset which varies distinct properties of output associated with hallucination. This includes output correctness, confidence, relevance, coherence, and completeness. We find that different geometric statistics capture different types of hallucinations. Along the way we show that many existing geometric detection methods have substantial sensitivity to shifts in task domain (e.g., math questions vs. history questions). Motivated by this, we introduce a simple normalization method to mitigate the effect of domain shift on geometric statistics, leading to AUROC gains of +34 points in multi-domain settings.

Problem

• hallucination
• geometric metrics
• large language models
• domain shift
• output properties

Innovation

• geometric hallucination detection
• domain shift
• synthetic dataset
• normalization method
• LLM internal representations